Abstract:

Elements of the matrix group GL(n) can be encoded by weighted planar networks (graphs with numbers written on edges/faces) with n sources and n sinks.  Such graphical representation is useful for studying matrix factorizations, totally positive matrices etc.  Furthermore, Gekhtman, Shapiro, and Vainshtein showed that such networks also capture Poisson geometry of GL(n) endowed with a standard multiplicative Poisson bracket.  In the talk I will present similar graphical representations of simple Lie groups of type B and C.